Low-energy electron diffraction (LEED) is considered as elastic electron-atom scattering (EEAS) operating in a target crystal waveguide, where a signal electron carrier wave is wavenumber modulated by signal exchange-correlation (XC) interaction. A carrier potential is designed using a KKR (Korringa-Kohn-Rostoker) muffin-tin (MT) model built on overlapping MT spheres that implement atoms with double degree of freedom, radius and potential level. An XC potential is constructed using Sernelius’s many-particle theory on electron self-energy. EEAS phase shifts are derived from Dirac’s differential equations, and four recent LEED investigations are recalculated: Cu(111) + (3 √ 3 × √ 3) R30°-TMB, TMB = 1,3,5-tris(4-mercaptophenyl)-benzene with chemical formula C24H15S3; Ag(111) + (4 × 4)-O; Ag(111) + (7 × √ 3)rect-SO4; and Ru(0001) + ( √ 3 × √ 3)R30°-Cl. Our EEAS phase shifts generate substantially improved reliability factors, and we report the first confirmation of electron self-energy by LEED experiment.